Improved successive approximation methods for discounted Markov decision processes

Successive Approximation (S.A.) methods, for solving discounted Markov decision problems, have been developed to avoid the extensive computations that are connected with linear programming and policy iteration techniques for solving large scaled problems. Several authors give such an S.A. algorithm. In this paper we introduce some new algorithms while furthermore it will be shown how the several S.A. algorithms may be combined. For each algorithm converging sequences of upper and lower bounds for the optimal value will be given

An upper bound on the number of non-unique assignments in relaxed (mixed) integer linear programs of the assignment type

An upper bound is given for the number of non-unique assignments when solving the linear programming relaxation of (mixed) integer linear programming problems in which the integer variables are governed by assignment type constraints. Key-words: (mixed) integer linear programming, assignment problems, class-room scheduling

Solving linear systems by methods based on a probabilistic interpretation

In this paper it is demonstrated how the probabilistic concept of a stopping time in a random process may be used to generate an iterative method for solving a system of linear equations. Actually all known iterative approximation methods for solving linear equations are generated by various choices of a stopping time e.g. the point and block Jacobi methods, the point and block Gauss-Seidel Methods and overrelaxation methods are covered. The probabilistic approach offers -in a natural way- the possibility of adapting the solution technique to the special structure of the problem. Moreover, posterior bounds for the solution are constructed, which lead to faster convergence of the approximations than with usual prior bounds

On using discrete random models within decision support systems

In this paper we review how models for discrete random systems may be used to support practical decision making. It will be demonstrated how organizational requirements determine to a large extent the type of model to be applied as well as the way in which the model should be applied. This demonstration is given via several practical examples of Markov chain models, cohort models, and Markov decision models. The examples are drawn from various areas ranging from the purely technical to social applications. It is demonstrated that the models that are needed for supporting the decision making process may vary from purely descriptive models to optimization models. Similarly, the obvious way of application of a model may vary from straightforward numerical analysis to interactive modelling procedures based upon managerial evaluation. It will also be demonstrated how the numerical methods to be used depend on the structure of the model as well as on applicational aspects. The numerical aspect is strongly related to the aforementioned aspects, since the model choiche heavily determines the computational possibilities

FORMASY : forecasting and recruitment in manpower systems

In this paper the tools are developed for forecasting and recruitment planning in a graded manpower system. Basic features of the presented approach are: - the system contains several grades or job categories in which the employees stay for a certain time before being promoted or leaving the system, - promotability and leaving rate for any employee depend on time spent in the job category and personal qualifications (like education, experience, age), - recruitment is not necessarily restricted to the lowest level ln the system, - several planning aims and restrictions are allowed. The approach is based on a generalized Markov model for the dynamic behaviour of an individual employee. On this Markov model a forecasting procedure and a recruitment-scheduling procedure are based

A note on dynamic programming with unbounded rewards

In a recent paper, Lippman presents sufficient conditions for Denardo's N-stage contraction in discounted semi-Markov decision processes with unbounded rewards. In this note it is demonstrated that Lippman's conditions may be replaced by weaker conditions which even imply 1-stage contraction. The verification of the conditions of this note is somewhat easier

A decision support system for location and allocation problems within a brewery

In this paper we describe a decision support system that was developed for supporting strategical and tactical decision making with respect to location of warehouses and the allocation of customers to warehouses. The system is currently used by the Department of "physical distributions" within Heineken breweries to help management with mid- and longterm logistic decisions. The core of the system is a large mixed integer linear programming model. This paper containes a (long) abstract of the research carried out. A complete description of the results will be submitted for publication elsewhere

E-Fulfillment and Multi-Channel Distribution – A Review

This review addresses the specific supply chain management issues of Internet fulfillment in a multi-channel environment. It provides a systematic overview of managerial planning tasks and reviews corresponding quantitative models. In this way, we aim to enhance the understanding of multi-channel e-fulfillment and to identify gaps between relevant managerial issues and academic literature, thereby indicating directions for future research. One of the recurrent patterns in today’s e-commerce operations is the combination of ‘bricks-and-clicks’, the integration of e-fulfillment into a portfolio of multiple alternative distribution channels. From a supply chain management perspective, multi-channel distribution provides opportunities for serving different customer segments, creating synergies, and exploiting economies of scale. However, in order to successfully exploit these opportunities companies need to master novel challenges. In particular, the design of a multi-channel distribution system requires a constant trade-off between process integration and separation across multiple channels. In addition, sales and operations decisions are ever more tightly intertwined as delivery and after-sales services are becoming key components of the product offering.Distribution;E-fulfillment;Literature Review;Online Retailing

A property of assignment type mixed integer linear programming problems

In this paper we will proof that rather tight upper bounds can be given for the number of non-unique assignments that are achieved after solving the linear programming relaxation of some types of mixed integer linear assignment problems. Since in these cases the number of splitted assignments is small a heuristic can be used to reach a practically good and feasible assignment. Moreover the type of proof can be exploited for related problems to investigate whether a linear programming relaxation will yield mainly integer assignments. Key words: mixed integer linear programming, assignment problems, location allocation problems, distribution problems

Integrating Closed-loop Supply Chains and Spare Parts Management at IBM

Ever more companies are recognizing the benefits of closed-loop supplychains that integrate product returns into business operations. IBMhas been among the pioneers seeking to unlock the value dormant inthese resources. We report on a project exploiting product returns asa source of spare parts. Key decisions include the choice of recoveryopportunities to use, the channel design, and the coordination ofalternative supply sources. We developed an analytic inventory controlmodel and a simulation model to address these issues. Our results showthat procurement cost savings largely outweigh reverse logistics costsand that information management is key to an efficient solution. Ourrecommendations provide a basis for significantly expanding the usageof the novel parts supply source, which allows for cutting procurementcosts.supply chain management;reverse logistics;product recovery;inventory management;service management